{"id":454,"date":"2026-05-05T04:46:40","date_gmt":"2026-05-05T04:46:40","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-nguyen-viet-xuan-vinh-phuc\/"},"modified":"2026-05-05T07:19:37","modified_gmt":"2026-05-05T07:19:37","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-nguyen-viet-xuan-vinh-phuc","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-nguyen-viet-xuan-vinh-phuc\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n Vi\u1ebft Xu\u00e2n V\u0129nh Ph\u00fac"},"content":{"rendered":"

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n Vi\u1ebft Xu\u00e2n V\u0129nh Ph\u00fac <\/strong>\u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n s\u00e1t v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 minh h\u1ecda c\u1ee7a B\u1ed9 GD&\u0110T, c\u00f3 t\u00ednh ph\u00e2n lo\u1ea1i cao v\u00e0 b\u00e1m s\u00e1t th\u1ef1c t\u1ebf \u00f4n luy\u1ec7n. \u0110\u00e2y l\u00e0 t\u00e0i li\u1ec7u tham kh\u1ea3o h\u1eefu \u00edch d\u00e0nh cho h\u1ecdc sinh l\u1edbp 12 trong qu\u00e1 tr\u00ecnh chu\u1ea9n b\u1ecb cho k\u1ef3 thi quan tr\u1ecdng s\u1eafp t\u1edbi. C\u00f9ng T\u00e0i Li\u1ec7u <\/strong>\u00d4n Thi<\/strong><\/a> kh\u00e1m ph\u00e1 \u0111\u1ec1 thi n\u00e0y c\u00f3 nh\u1eefng c\u00e2u h\u1ecfi g\u00ec \u0111\u1eb7c bi\u1ec7t.<\/p>\n

N\u1ed9i dung \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n Vi\u1ebft Xu\u00e2n V\u0129nh Ph\u00fac<\/span><\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n Vi\u1ebft Xu\u00e2n V\u0129nh Ph\u00fac <\/strong>\u0111\u00e1nh gi\u00e1 to\u00e0n di\u1ec7n ki\u1ebfn th\u1ee9c v\u00e0 k\u1ef9 n\u0103ng c\u1ee7a h\u1ecdc sinh l\u1edbp 12, \u0111\u1ed3ng th\u1eddi gi\u00fap c\u00e1c em l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac v\u00e0 m\u1ee9c \u0111\u1ed9 kh\u00f3 c\u1ee7a k\u1ef3 thi ch\u00ednh th\u1ee9c. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi \u0111\u01b0\u1ee3c tr\u00edch tr\u1ef1c ti\u1ebfp trong \u0111\u1ec1 thi:<\/p>\n

PH\u1ea6N I: C\u00e2u tr\u1eafc nghi\u1ec7m nhi\u1ec1u ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn<\/strong><\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd:<\/p>\n

\"\"<\/p>\n

\u0110i\u1ec3m c\u1ef1c \u0111\u1ea1i c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 l\u00e0<\/p>\n

A. x = -1 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. y = 4 .\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. (-1; 4) . \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. x = 1 .<\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 h\u00ecnh v\u1ebd:<\/p>\n

\"\"<\/p>\n

Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y sai?<\/p>\n

A. H\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 c\u00f3 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t b\u1eb1ng -2 .
\nB. H\u00e0m s\u1ed1 c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb.
\nC. \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 hai ti\u1ec7m c\u1eadn ngang.
\nD. H\u00e0m s\u1ed1 c\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t b\u1eb1ng 5 v\u00e0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t b\u1eb1ng -2 .<\/p>\n

PH\u1ea6N II: C\u00e2u tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<\/strong><\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = f(x) = (ax\u00b2 + bx + c)\/(dx + e) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean sau<\/p>\n

\"\"<\/p>\n

a) H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean c\u00e1c kho\u1ea3ng (-\u221e; -1) v\u00e0 (3; +\u221e) .<\/p>\n

b) Gi\u00e1 tr\u1ecb c\u1ef1c \u0111\u1ea1i c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 y = 3 .<\/p>\n

c) Ti\u1ec7m c\u1eadn xi\u00ean c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh y = mx + n , khi \u0111\u00f3 m > 0 .<\/p>\n

d) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m c\u00f3 tung \u0111\u1ed9 \u00e2m.<\/p>\n

C\u00e2u 2.<\/strong> Cho hai h\u00e0m s\u1ed1 f(x) = x\u00b3 v\u00e0 g(x) = \u221a[3]x .<\/p>\n

a) int [f(x) – g(x)] dx = (x\u2074)\/(4) – 3\/4 x \u221a[3]x + C .<\/p>\n

b) N\u1ebfu F(x) l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a f(x) v\u00e0 F(1) = 1 , th\u00ec F(x) = 1\/4 x\u2074 + 3\/4 x .<\/p>\n

c) int\u2080\u00b9 f(x) dx = 3\/4 .<\/p>\n

d) M\u1ed9t vi\u00ean g\u1ea1ch men c\u00f3 d\u1ea1ng h\u00ecnh vu\u00f4ng OABC c\u1ea1nh l\u00e0 1. Khi ch\u1ecdn h\u1ec7 tr\u1ee5c Oxy nh\u01b0 h\u00ecnh v\u1ebd th\u00ec hai \u0111\u01b0\u1eddng cong bao quanh ph\u1ea7n t\u00f4 \u0111\u1eadm tr\u00ean vi\u00ean g\u1ea1ch t\u01b0\u01a1ng \u1ee9ng l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 y = x\u00b3 v\u00e0 y = \u221a[3]x . Di\u1ec7n t\u00edch ph\u1ea7n kh\u00f4ng \u0111\u01b0\u1ee3c t\u00f4 \u0111\u1eadm tr\u00ean vi\u00ean g\u1ea1ch men c\u00f3 gi\u00e1 tr\u1ecb b\u1eb1ng 1\/2 (dvdt).<\/p>\n

\"\"<\/p>\n

PH\u1ea6N III: C\u00e2u tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/p>\n

C\u00e2u 1.<\/strong> M\u1ed9t doanh nghi\u1ec7p t\u01b0 nh\u00e2n A chuy\u00ean kinh doanh xe g\u1eafn m\u00e1y c\u00e1c lo\u1ea1i. Hi\u1ec7n nay doanh nghi\u1ec7p \u0111ang t\u1eadp trung v\u00e0o chi\u1ebfn l\u01b0\u1ee3c kinh doanh xe X v\u1edbi chi ph\u00ed mua v\u00e0o m\u1ed9t chi\u1ebfc l\u00e0 27 tri\u1ec7u \u0111\u1ed3ng v\u00e0 b\u00e1n ra v\u1edbi gi\u00e1 31 tri\u1ec7u \u0111\u1ed3ng. V\u1edbi gi\u00e1 b\u00e1n n\u00e0y, s\u1ed1 l\u01b0\u1ee3ng xe m\u00e0 kh\u00e1ch h\u00e0ng \u0111\u00e3 mua trong m\u1ed9t n\u0103m l\u00e0 600 chi\u1ebfc. Nh\u1eb1m m\u1ee5c ti\u00eau \u0111\u1ea9y m\u1ea1nh h\u01a1n n\u1eefa l\u01b0\u1ee3ng ti\u00eau th\u1ee5 d\u00f2ng xe \u0111ang b\u00e1n ch\u1ea1y n\u00e0y, doanh nghi\u1ec7p d\u1ef1 \u0111\u1ecbnh gi\u1ea3m gi\u00e1 b\u00e1n. B\u1ed9 ph\u1eadn nghi\u00ean c\u1ee9u th\u1ecb tr\u01b0\u1eddng \u01b0\u1edbc t\u00ednh r\u1eb1ng n\u1ebfu gi\u1ea3m 1 tri\u1ec7u \u0111\u1ed3ng m\u1ed7i chi\u1ebfc xe th\u00ec s\u1ed1 l\u01b0\u1ee3ng xe b\u00e1n ra trong m\u1ed9t n\u0103m s\u1ebd t\u0103ng th\u00eam 200 chi\u1ebfc. H\u1ecfi theo \u0111\u00f3, gi\u00e1 b\u00e1n m\u1edbi l\u00e0 bao nhi\u00eau tri\u1ec7u \u0111\u1ed3ng th\u00ec l\u1ee3i nhu\u1eadn thu \u0111\u01b0\u1ee3c cao nh\u1ea5t?<\/p>\n

C\u00e2u 2.<\/strong> M\u1ed9t t\u1ea5m k\u00ednh l\u00e0m m\u1eb7t b\u00e0n (H1) c\u00f3 h\u00ecnh d\u00e1ng tam gi\u00e1c \u0111\u1ec1u v\u1edbi 3 \u0111\u1ec9nh \u0111\u01b0\u1ee3c l\u00e0m cong (H2). Bi\u1ebft c\u1ea1nh t\u1ea5m k\u00ednh tam gi\u00e1c ban \u0111\u1ea7u b\u1eb1ng 12 (dm). \u0110\u1ec3 c\u1eaft g\u00f3c b\u00e0n \u0111\u01b0\u1ee3c \u0111\u1eb9p th\u00ec ng\u01b0\u1eddi ta c\u1eaft theo \u0111\u01b0\u1eddng cong l\u00e0 \u0111\u01b0\u1eddng Parabol (P): y = -(\u221a3)\/(4)x\u00b2 + 5\u221a3 . (H3) c\u00f3 hai nh\u00e1nh ti\u1ebfp gi\u00e1p v\u1edbi hai c\u1ea1nh c\u1ee7a tam gi\u00e1c (H4).<\/p>\n

T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n Vi\u1ebft Xu\u00e2n V\u0129nh Ph\u00fac<\/strong><\/h2>\n

V\u1edbi c\u1ea5u tr\u00fac b\u00e1m s\u00e1t \u0111\u1ec1 minh h\u1ecda, m\u1ee9c \u0111\u1ed9 ph\u00e2n h\u00f3a h\u1ee3p l\u00fd v\u00e0 n\u1ed9i dung ph\u1ee7 r\u1ed9ng c\u00e1c chuy\u00ean \u0111\u1ec1 tr\u1ecdng t\u00e2m, \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT Nguy\u1ec5n Vi\u1ebft Xu\u00e2n V\u0129nh Ph\u00fac<\/strong> l\u00e0 t\u00e0i li\u1ec7u \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3, gi\u00fap h\u1ecdc sinh l\u1edbp 12 c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c v\u00e0 n\u00e2ng cao k\u1ef9 n\u0103ng l\u00e0m b\u00e0i. C\u00e1c em h\u1ecdc sinh c\u00f3 th\u1ec3 t\u1ea3i file \u0111\u1ec1 thi th\u1eed thpt qu\u1ed1c gia m\u00f4n to\u00e1n 2025<\/a> k\u00e8m \u0111\u00e1p \u00e1n chi ti\u1ebft \u1edf \u0111\u01b0\u1eddng d\u1eabn d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 tham kh\u1ea3o v\u00e0 luy\u1ec7n t\u1eadp th\u00eam.<\/p>\n